Solve x^2 - 6x + 2 = 0 by completing the square

Problem: Solve $x^2 - 6x + 2 = 0$ by completing the square.

Steps

1. Subtract 2 from both sides
   $$x^2 - 6x = -2$$
2. Add the square of half the coefficient of $x$ to both sides
   $$x^2 - 6x + 9 = -2 + 9$$
3. Factor the left side and simplify the right side
   $$(x - 3)^2 = 7$$
4. Take the square root of both sides
   $$x - 3 = \pm\sqrt{7}$$
5. Add 3 to both sides
   $$x = 3 \pm\sqrt{7}$$